Must the prayer be repeated if there was a doubt about something – water or urine – having been discharged after relieving oneself, and this was remembered after the prayer?

If your feeling that something has exited the private part is merely a doubt, then do not pay attention to it. There is no need to cleanse the area because impurity is not determined by mere doubt. However, if you are certain that something has exited, yet you doubt whether it is pure or impure, you are not required to cleanse it for the same reason. But if you are certain that it is urine or water that came out of the urinary tract, then it is obligatory to cleanse it. If you did not do so until you performed ablution and prayed, the preponderant opinion is that your prayer is valid, because avoiding impurity is a condition when one knows and is able. And whoever forgot an impurity on their body or clothes and prayed, their prayer is valid.